Using the intensities of individual H2CO lines to constrain the kinetic temperature and spatial densities can be error-fraught due to large absolute calibration uncertainties and beam-filling factor. Thus, we opted to use line ratios instead. The relative populations of the H2CO rotational energy levels in different \(K_{\rm a}\)  ladders are predominantly governed by collisions since dipole selection rules dictate that \(\Delta K = 0\)  for radiative excitation; hence, ratios of line fluxes involving different \(K_{\rm a}\)  ladders are good tracers of the kinetic temperature. On the other hand, line ratios involving lines emitted from within the same \(K_{\rm a}\)  ladders yield estimates of the spatial density of the gas [1]}.
We excluded the collisions with electrons and atomic hydrogen in our RADEX analysis because they are not expected to have a significant contribution in comparison to H2. The abundance ratio of electrons (\(x(e)= n(e)/n({H2}) \lesssim 10^{-5}\) ) should not be large given that the gas has undergone a \(C\) -type shock [2]}. Observations of W28 by [3]} showed that overall molecular hydrogen is at least three times more abundant than H I in the SNR as a whole. Hence, neglecting collisions with electrons and hydrogen atoms is justified. Nevertheless, [4]} did not find a significant difference in results from including collisions from these species in their similar analysis of SNR IC 443 either.
